Short Answer TypeIn how many ways can 5 girls be seated in a row so that two girls Ridhi and Sanya are:
(a) always together (b) never together
Number of digits = 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Number of digits used = 4
Number of permutations in which at least one digit is reveresed = x - y ...(i)
where x = number of permutations when any digit may be repeated any number of times,
y = number of permutations when no digit is repeated.
From part (a), x = 9000
From part (b), y = 4536.
Hence, the number of 4-digit numbers in which at least one digit is repeated.
= 9000 - 4536 = 4464
Long Answer Type(b) there is no restriction as to the number of prizes that a boy may get.
(c) no boy sets all prizes.
There are 8 students appearing for an examination, of which 3 appear in mathematics paper, and 5 in other different subjects. In how many ways can they be seated if
(a) all the students appearing for mathematics paper are together.
(b) the students appearing for mathematics paper are not all together.
(c) no two students appearing in mathematics paper are seated together ?
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